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A052243
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Initial prime in set of (at least) 4 consecutive primes in arithmetic progression with difference 30.
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23
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642427, 1058861, 3431903, 4176587, 4560121, 4721047, 5072269, 5145403, 5669099, 5893141, 6248969, 6285047, 6503179, 6682969, 8545357, 8776121, 8778739, 9490571, 9836227, 9843019, 9843049, 10023787, 11697979, 12057919, 12340313, 12687119, 12794641, 12845849
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OFFSET
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1,1
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COMMENTS
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Primes p such that p, p+30, p+60, p+90 are consecutive primes.
The analogous sequence for a CPAP-5 (at least five consecutive primes in arithmetic progression) with gap 30 does not have its own entry in the OEIS, but for over 500 terms it is identical to A059044. The CPAP-6 analog is A058362. - M. F. Hasler, Jan 02 2020
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LINKS
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FORMULA
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EXAMPLE
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642427, 642457, 642487, 642517 are consecutive primes, so 642427 is in the sequence.
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MAPLE
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p := 2 : q := 3 : r := 5 : s := 7 : for i from 1 do if q-p = 30 and r-q=30 and s-r=30 then printf("%d, \n", p) ; fi ; p := q ; q := r ; r := s ; s := nextprime(r) ; od: # R. J. Mathar, Apr 12 2008
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MATHEMATICA
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p=2; q=3; r=5; s=7; A052243 = Reap[For[i=1, i<1000000, i++, If[ q-p == 30 && r-q == 30 && s-r == 30 , Print[p]; Sow[p]]; p=q; q=r; r=s; s=NextPrime[r]]][[2, 1]] (* Jean-François Alcover, Jun 28 2012, after R. J. Mathar *)
Transpose[Select[Partition[Prime[Range[1100000]], 4, 1], Union[ Differences[#]] =={30}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *)
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PROG
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(PARI) A052243(n, p=2, print_all=0, g=30, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, print_all&& print1(o-g", "); n--||break); o=q-g); o-g} \\ optional 2nd arg specifies starting point, allows to define:
(Magma) f:=func<n|NextPrime(n)>; a:=[]; for p in PrimesInInterval(2, 13000000) do if (f(p)-p eq 30) and (f(f(p))-p eq 60) and (f(f(f(p)))-p eq 90) then Append(~a, p); end if; end for; a; // Marius A. Burtea, Jan 04 2020
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CROSSREFS
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Subsequence of A052195 and of A054800 (start of CPAP-4 with any common difference).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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